This paper presents a fast and rigorous design method for grating-based metal-free polarizing filter applications using two-step hybrid optimization techniques. Grating structures utilizing the total internal reflection in a lamellar configuration were used to achieve metal-free solution, which is a key technology in the chirped pulse amplification for high power laser system. Here two polarizing filters were designed: polarization sensitive and polarization insensitive. Those polarization performances were characterized by the rigorous coupled-wave analysis (RCWA), and the design parameters of grating structures, pitch, depth, and filling factor were optimized by two-step hybrid optimization procedure because the diffraction characteristics of grating-based polarizing filters are highly sensitive to small changes in design parameters. The Taguchi method is incorporated into selection process in the genetic algorithm, which indicates that the Taguchi method optimizes the design parameters in a coarse manner, and then, coarsely optimized parameters are finely optimized using the genetic algorithm. Therefore the proposed method could solve global numerical optimization problems with continuous variables. The proposed two-step hybrid optimization algorithm could effectively optimize the grating structures for the purpose of polarization filter applications, and the optimized grating structures could selectively filter the incident light up to 99.8% as to TE or TM waves.

Diffraction gratings play an important role in many optical applications, including optical telecommunications components, spectroscopy, and the chirped pulse amplification (CPA) for a high power laser system [

Scalar diffraction theory is one of the widely used methods for the design and analysis of grating structures [

In general, diffraction gratings with a lamellar configuration consist of a periodically varying boundary of the period

Schematic of the TIR gratings in a lamellar configuration.

RCWA is one of direct methods to solve the Maxwell’s equations based on a state space representation without any assumptions [

The following optimization problem is considered:

The genetic algorithm is a class of adaptive stochastic optimization algorithms involving search and optimization [

The proposed HTGA optimization procedure was illustrated in Figure

Optimization procedure of HTGA.

The hybrid optimization procedure was performed to achieve polarizing-sensitive performance from the TIR-based grating structures, and each of the design parameters was carefully chosen. The pitch parameter was set from (

Efficiency (a) and parameter (b) convergence curves of HTGA with respect to generation number for the TIR-based gratings with polarization-sensitive performance.

Efficiency (a) and parameter (b) convergence curves of a pure GA with respect to generation number for the TIR-based gratings with polarization-sensitive performance.

Spectral response curves on the results of the Taguchi method only

Efficiency curves with respect to parameter errors of the TIR-based gratings with polarization-sensitive performance.

In the same manner with a previous process, the hybrid optimization procedure was performed to achieve polarizing-insensitive performance from the TIR-based grating structures. The pitch parameter was set from (

Efficiency (a) and parameter (b) convergence curves of HTGA with respect to generation number for the TIR-based gratings with polarization-insensitive performance.

Efficiency (a) and parameter (b) convergence curves of a pure GA with respect to generation number for the TIR-based gratings with polarization-insensitive performance.

Spectral response curves on the results of the Taguchi method only

Efficiency curves with respect to parameter errors of the TIR-based gratings with polarization-insensitive performance.

We have demonstrated the fast and rigorous multiobjective HTGA optimization procedure, which could solve global numerical optimization problems with continuous variables. This method was applied to optimization of the TIR-based grating structures for polarizing filter applications that the diffraction characteristics are high sensitive to those geometric properties, pitch, filling factor, and depth. RCWA was combined with the hybrid optimization methods to evaluate the performance of the TIR-based grating structure and find out the optimal set of design parameters at the same time. The proposed method could effectively optimize the grating structures for the purpose of polarization filter applications, and the optimized grating structures could selectively filter the incident light up to 99.8% as to TE or TM waves. The result showed its performance with high accuracy and less computation time compared to that by a single optimization technique. As a result, HTGA was confirmed as the proper optimization technique to provide the global minimum with high reproducibility, no failure, and less computation time in highly sensitive optimization problems. For the future work, the Taguchi method will be incorporated crossover and mutation process to select better set of parameters in a whole feasible space promptly.

The author declares that there is no conflict of interests regarding the publication of this paper.